The invention is based on a cutting tool for working interior and exterior contours of workpieces, with the tool including at least one cutting plate exchangeably fastened to a basic tool body and being adjustable radially to the tool axis by means of at least one adjustment screw while being clampable by clamping means to a supporting shoulder of the basic tool body that absorbs the working pressure. In a prior art cutting tool of this type (German Patent 3,201,508), a separate screw element is provided to adjust the cutting plate and to clamp it tightly into the supporting shoulder of the basic tool body. The cutting plate is disposed at a clamping shoe which is supported in the basic tool body so as to be rotatable about an axis that is axially and radially offset relative to the cutting plate. The radial adjustment of the cutting plate relative to the tool axis is effected by rotating the clamping shoe relative to the basic tool body, with this inevitably also changing the angular position of the cutting plate relative to the tool axis. To clamp the cutting plate or cutting edge to the supporting shoulder of the basic tool body, the clamping shoe is pulled at a right angle against the supporting shoulder, whereupon the cutting plate is held at the basic tool body by a friction lock. This configuration requires a relatively large amount of space and is therefore unsuitable for tools with which very small bores are to be worked. Moreover, the prior art arrangement is also unsuitable for high-speed work because the cutting plate is not held in a form lock at the basic tool body to prevent it from radially escaping from the revolving tool.